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PC-Based Sensitivity Analysis of the Basic Reproduction Number of Population and Epidemic Models

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Current Trends in Dynamical Systems in Biology and Natural Sciences

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 21))

Abstract

The basic reproduction number, simply denoted by R 0, plays a fundamental role in the analysis of population and epidemic models. However in mathematical modelling the specification of the input parameters can be crucial since, due to some limitations in experimental data available, they can be uncertain and often represented as random quantities in a suitable probabilistic framework. In this context the Polynomial Chaos Expansions (PCEs), coupled with suitable numerical methods, furnish important tools for the sensitivity analysis and the uncertainty quantification of the random model response. The aim of this paper is to describe how the variability of R 0 is affected by the variability of the input parameters, through the evaluation of Sobol’ indices by PC-based methods. The use of a suitable and new computational model of R 0 allows also to consider more complex epidemic models, where R 0 is defined as the spectral radius of the infinite-diminensional next generation operator. The efficiency and versatility of the numerical approach are confirmed by the experimental analysis of two examples of increasing complexity.

The author “Rossana Vermiglio” was a member of the INdAM Research group GNCS.

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Author information

Authors and Affiliations

  1. University of Zürich, Institute of Mathematics, Zürich, Switzerland

    Francesco Florian

  2. Member of CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy

    Francesco Florian

  3. CDLab - Computational Dynamics Laboratory, Department of Mathematics, Computer Science and Physics, University of Udine, Udine, Italy

    Rossana Vermiglio

Authors
  1. Francesco Florian
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  2. Rossana Vermiglio
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Corresponding author

Correspondence to Rossana Vermiglio .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Trento, Trento, Italy

    Maira Aguiar

  2. Department of Mathematics, University of Évora, Évora, Portugal

    Carlos Braumann

  3. Faculty of Science, VU University Amsterdam, Amsterdam, The Netherlands

    Bob W. Kooi

  4. Department of Mathematics, University of Trento, Trento, Italy

    Andrea Pugliese

  5. Department of Mathematics “CMAF-CIO”, University of Lisbon, Lisbon, Portugal

    Nico Stollenwerk

  6. Department of Mathematics “Giuseppe Peano”, University of Turin, Torino, Italy

    Ezio Venturino

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Florian, F., Vermiglio, R. (2020). PC-Based Sensitivity Analysis of the Basic Reproduction Number of Population and Epidemic Models. In: Aguiar, M., Braumann, C., Kooi, B., Pugliese, A., Stollenwerk, N., Venturino, E. (eds) Current Trends in Dynamical Systems in Biology and Natural Sciences. SEMA SIMAI Springer Series, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-030-41120-6_11

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